Details

sample159.0ms

Algorithm

intervals

Results

55.0ms	44×	body	640	valid
32.0ms	57×	body	1280	valid
13.0ms	123×	body	80	valid
6.0ms	23×	body	320	valid
2.0ms	9×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	22	14
3	29	14
4	37	14
5	42	14
6	44	14
done	44	14

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (tan x) (tan x) 1.0)
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`difference-of-squares`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff` `associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

1.0ms	(fma (tan x) (tan x) 1.0)
29.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
13.0ms	(- 1.0 (* (tan x) (tan x)))
51.0ms	(* (tan x) (tan x))

series348.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma (tan x) (tan x) 1.0)
169.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
49.0ms	(- 1.0 (* (tan x) (tan x)))
58.0ms	(* (tan x) (tan x))

simplify3.1s

Counts

109 → 109

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	155	1557
1	330	1462
2	891	1345
3	2810	1320
done	5000	1314

prune545.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

4.0ms	(pow (cos x) 2)
4.0ms	(pow (cos x) 2)
4.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)

series89.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (cos x) 2)
18.0ms	(pow (cos x) 2)
21.0ms	(pow (sin x) 2)
31.0ms	(pow (sin x) 2)

simplify3.2s

Counts

92 → 92

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	68	616
1	138	530
2	293	466
3	807	466
4	3813	458
done	5000	458

prune478.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
0.2b	(fma (tan x) (tan x) 1.0)
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
76×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
13×	`difference-of-squares`
12×	`pow1`
11×	`add-cbrt-cube`
9×	`associate-/r/`
7×	`div-exp`
6×	`add-log-exp`
5×	`flip3--` `flip--` `div-inv`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`pow2` `frac-times` `sub-neg` `pow-flip` `frac-2neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

25.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
1.0ms	(fma (tan x) (tan x) 1.0)
11.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(* (tan x) (tan x))

series337.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
60.0ms	(fma (tan x) (tan x) 1.0)
60.0ms	(- 1.0 (* (tan x) (tan x)))
58.0ms	(* (tan x) (tan x))

simplify3.0s

Counts

171 → 171

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	270	3573
1	557	3211
2	1270	2917
3	3681	2794
done	5000	2785

prune479.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (fma (tan x) (tan x) 1.0)))
0.2b	(/ 1 (fma (tan x) (tan x) 1.0))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
16×	`associate-r`
14×	`pow1`
13×	`add-cbrt-cube`
7×	`associate-l`
6×	`add-log-exp`
5×	`prod-exp`
4×	`tan-quot` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `unswap-sqr`
3×	`frac-times` `flip3--` `fma-neg` `swap-sqr` `prod-diff` `associate-l/` `associate-/r` `flip--` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `div-inv` `difference-of-squares`
1×	`pow2` `sub-neg` `pow-flip` `frac-2neg` `pow-plus` `diff-log` `clear-num` `pow-sqr` `un-div-inv` `pow-prod-up` `inv-pow`

Counts

4 → 127

Calls

4 calls:

34.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (fma (tan x) (tan x) 1.0)))
5.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
7.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))

series376.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (fma (tan x) (tan x) 1.0)))
109.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
42.0ms	(- 1.0 (* (tan x) (tan x)))
44.0ms	(* (tan x) (tan x))

simplify3.3s

Counts

139 → 139

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	189	2015
1	398	1781
2	1086	1587
3	3660	1550
done	5000	1546

prune399.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes141.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	12	16
done	12	16

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.8s	1570×	body	1280	valid
1.2s	4235×	body	80	valid
839.0ms	1219×	body	640	valid
532.0ms	335×	body	160	valid
387.0ms	641×	body	320	valid